Portfolio Investment With Profitability As Fuzzy Numbers And An Example In Practice

As been well known, portfolio investment can effectively reduce the investment risk. From last mid-century to today, investment research has always been a hot issue, which has played a guiding role on investors. Therefore, it is very important to research its related theory. As China's special national conditions, China's securities market and stock market transactions are different from Western capitalism. As a result, we need to further study the proper portfolio investment model which can be suitable to China's securities market.Stochastic and fuzzy are two main aspects of the uncertainty in the financial market. The uncertainty of securities' return rate is the case. The financial market is characterized by fuzziness because of an investor's subjective judgment. In this paper, profitability is been as fuzzy numbers, in practice, which is consistent with the psychological state of investors. To satisfy investors' different psychological states, combined with fuzzy numbers, three models dealing with China's securities market are proposed, which are generalized from the Markowitz model. The three models can well meet the different needs of investors preferences, shown as follows:(1) revenue maximization model with profitability as fuzzy numbers;(2) risk minimization model with profitability as fuzzy numbers;(3) The optimal portfolio model with profitability as fuzzy numbers;As the model contains a nonlinear part of the planning, In addition, the software of Lingo is employed to solve the optimization, and Calculate the proportion of portfolio investment。Finally, combined with the characteristics of China's stock market, an example in practice is analyzed. The example shows its effective of the proposed models.